rtqichen/torchdiffeq
Torchdiffeq
torchdiffeq 是一个 PyTorch ODE（常微分方程）求解器库，专为解决初值问题和构建神经 ODE 框架而设计。它提供了一个可微分的 ODE 积分器，允许深度学习模型通过随时间积分动力学函数来模拟连续深度。
该库具有用于内存高效反向传播的伴随法梯度计算器。通过在时间上反向求解增广伴随系统，它可以在不存储每个中间求解器状态的情况下计算参数梯度。
该项目涵盖了具有自适应和固定步长求解器的数值积分，并结合了误差控制和多项式状态插值。它还支持可微分事件管理，以便在特定标量函数触发时终止求解器，并沿事件时间传播梯度。
该框架常用于连续归一化流以及通过学习连续时间常微分方程进行概率分布转换等应用。
Features
- Memory-Efficient - Uses the adjoint method to compute gradients without storing every intermediate solver state.
- ODE-Based - Calculates gradients through ODE solvers using either direct backpropagation or the adjoint method.
- Adjoint Gradient Calculation - Performs memory-efficient backward passes using an adjoint solver to determine parameter gradients.
- Simulation Gradient Computations - Computes loss function gradients by solving an augmented adjoint system backwards in time to optimize memory.
- Neural Dynamics Models - Trains deep learning networks with continuous depth by integrating dynamics functions over a time interval.
- Neural ODE Frameworks - Provides a framework for building deep learning models that simulate continuous depth by integrating dynamics functions over time.
- Simulation Adjoint Kernels - Provides a memory-efficient adjoint method to compute gradients by solving a second differential equation backwards in time.
- Differentiable ODE Integrators - Computes system trajectories and propagates gradients through adaptive or fixed-step numerical solvers.
- Ordinary Differential Equation Solving - Computes solutions to initial value problems using adaptive or fixed-step ordinary differential equation solvers.
- Initial Value Problem Solvers - Computes the solution to initial value problems using adaptive or fixed-step solvers with configurable tolerances.
- Continuous-Depth Network Simulation - Integrates a dynamics function over a time interval to simulate a neural network containing an infinite number of layers.
- Differentiable Solver Termination - Supports terminating solvers exactly when specific scalar functions cross zero and propagates gradients through the event time.
- Differentiable Event Management - Provides a way to stop solvers based on event functions while propagating gradients through the stop time.
- Differentiable Event Simulation - Stops a differential equation solver when specific event functions trigger and propagates gradients through the event time.
- Event-Based Termination - Implements solver termination triggered by specific event functions with exact gradient computation at the stop time.
- Tensor Computation Graphs - Integrates with PyTorch's automatic differentiation engine to track operations and compute gradients across continuous-time dynamics.
- Integration Error Control - Adjusts adaptive solver step sizes using absolute and relative error tolerances to maintain numerical precision.
- Continuous-Time Density Transformations - Transforms simple probability distributions into complex densities by applying learned continuous-time ordinary differential equations.
- Continuous Normalizing Flows - Transforms simple distributions into complex densities by applying learned continuous-time ordinary differential equations.
- Adaptive-Step Integrators - Implements adaptive stepping to maintain numerical precision by adjusting intervals based on local error estimates.
- 计算机视觉 - Neural ordinary differential equations for continuous-depth models.
- Data Processing - Learning neural event functions for ordinary differential equations.
- Neural Differential Equations - Framework for neural ordinary differential equations.
- Data and Graph Processing - Solver for ordinary differential equations.
- 开发者工具 - Differentiable ODE solvers.
